Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;

public class Solution
{
	static InputReader in = new InputReader(System.in);
	static int mod = (int)1e9 + 7;
	
    public static void main(String args[]) {
        new Thread(null, new Runnable() {
            public void run() {
                try{
                    solve();
                }
                catch(Exception e){
                    e.printStackTrace();
                }
            }
        }, "1", 1 << 26).start();
    }
    
    public static void solve(){
		int n = in.nextInt();
		int[] ar = new int[n];
		int sum = 0;
		int indexOfOdd = -1;
		int minIndex = 0;
		int minElement = ar[0];
		for(int i = 0; i < n; i++) {
			ar[i] = in.nextInt();
			sum += ar[i];
			if(ar[i] % 2 != 0) indexOfOdd = i;
			if(ar[i] < minElement) {
				minElement = ar[i];
				minIndex = i;
			}
		}
		
    	if(sum % 2 != 0) {
    		System.out.println(0);
    	} else {
    		if(!isPossible(ar, n)) {
    			System.out.println(0);
    			return;
    		}
    		
    		if(indexOfOdd != -1) {
    			System.out.println(1);
    			System.out.println(indexOfOdd + 1);
    			return;
    		}
    		
    		System.out.println(1);
    		for(int i = 0; i < n; i++) {
    			int[] newArr = new int[n - 1];
    			int k = 0;
    			for(int j = 0; j < n; j++) {
    				if(i == j) continue;
    				newArr[k++] = ar[j];
    			}
    			
    			if(!isPossible(newArr, n - 1)) {
    				System.out.println(i + 1);
    				return;
    			}
    		}
    	}
    		
    }
   
    private static boolean isPossible(int[] arr, int n) {
    	int i, j, sum = 0;
    	for (i = 0; i < n; i++)
    	sum += arr[i];

    	if (sum % 2 != 0)
    	return false;

    	boolean part[][] = new boolean[n + 1][sum / 2 + 1];

    	for (i = 0; i <= sum/2; i++)
            part[0][i] = false;

    	for (i = 0; i <= n; i++)
    	part[i][0] = true;

    	// Fill the partition table in botton up manner
    	for (i = 1; i <= n; i++){
    		for (j = 1; j <= sum/2; j++){
    			part[i][j] = part[i-1][j];
    			if (j >= arr[i - 1])
    			part[i][j] = part[i][j] ||
    						part[i - 1][j - arr[i -1]];

    		}
    	}

    	return part[n][sum/2];
	}

	/*TEMPLATE*/
    
    //MATHS
    static int gcd(int a, int b) {
    	return (b==0)?a:gcd(b,a%b);
    }
    
    static long binPow(long x, long y) {
        long ans = 1L;
        while(y > 0) {
            if(y % 2 == 1)
                ans = mul(ans, x);
            x = mul(x, x);
            y /= 2;
        }
        return ans;
    }
    
    static long add(long x, long y) {
    	x += y;
    	return mod(x, mod);
    }
    
    static long mul(long x, long y) {
    	return mod(x * y, mod);
    }
    
    static long divide(long x, long y) {
        return mul(x, binPow(y, mod - 2));
    }

    static long mod(long x, long p) {
        x %= p;
        if (x < 0)
            x += p;
        return x;
    }
        
    public static int[] spf(int maxn) {
    	int[] spf=new int[maxn+1];
    	spf[0]=spf[1]=1;
    	for(int i=2;i<=maxn;i++) {
    		if(i%2==0) spf[i]=2;
    		else 
    			spf[i]=i;
    	}
    	for(int i=3;i*i<=maxn;i++) {
    		if(spf[i]==i){
    			for (int j=i*i; j<=maxn; j+=i) 
                    if (spf[j]==j) 
                        spf[j] = i;
    		}
    	}
    	return spf;
    }
    
    //ARRAYS
    public static int[] intArray(int n) {
    	int ar[]=new int[n];
    	for(int i=0;i<n;i++)
    		ar[i]=in.nextInt();
    	return ar;
    }
    
    public static void swap(int i, int j, int ar[]) {
    	int c=ar[i];ar[i]=ar[j];ar[j]=c;
    }
    
    public static void reverse(int ar[]) {
    	int l=0, r=ar.length-1;
    	while(l<r) {
    		int temp=ar[l]; ar[l]=ar[r]; ar[r]=temp;
    		l++; r--;
    	}
    }
    
    public static int upperBound(int[] array, int value) {
    	//return next higher element. If greater than all elements then returns array.length
    	//returns 0 if smaller than all elements
    	int low = 0;
    	int high = array.length;
    	while (low < high) {
    		final int mid = (low + high) / 2;
    		if (value >= array[mid]) {
    			low = mid + 1;
    		} else {
    			high = mid;
    		}
    	}
    	return low;
    }
    
    public static int lowerBound(int[] array, int value) {
    	//Returns first occurrence.
    	//Bigger than all elements then return array.length
    	//Not found, then next greater.s
    	int low = 0;
    	int high = array.length;
    	while (low < high) {
    		final int mid = (low + high) / 2;
			if (value <= array[mid]) {
			high = mid;
			} else {
				low = mid + 1;
			}
    	}
    	return low;
	}
    
    public static void pn(Object o) {
      System.out.println(o);
    }
    
    static class InputReader {
 
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int snumChars;
        private SpaceCharFilter filter;
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
 
        public int snext() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
 
        public int nextInt() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
 
            int res = 0;
 
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
 
            return res * sgn;
        }
 
        public long nextLong() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = snext();
            }
 
            long res = 0;
 
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = snext();
            } while (!isSpaceChar(c));
 
            return res * sgn;
        }
 
        public String readString() {
            int c = snext();
            while (isSpaceChar(c))
                c = snext();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = snext();
            } while (!isSpaceChar(c));
            return res.toString();
        }
 
        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}